Theoretical calculations were carried out for the isomeric di-1,2,3,4-tetrazine tetraoxides (DTTO and iso-DTTO). The most important explosion performance parameters, the detonation pressure and detonation velocity, are dominated by the densities and not by the heats of formation of these compounds. Since DTTO and iso-DTTO are unknown, reliable predictions of their crystal densities are crucial for an evaluation of the potential of these materials as explosives. In this study, the crystal densities were predicted using both Ammon's Atom/Functional Group and Atom Code Volume Additivity Parameters and Quantum Mechanical molecular Volume methods, resulting in similar densities and explosion parameters. Although the likely uncertainties in our predicted density values are difficult to assess due to a lack of experimental data for closely related known compounds, our results demonstrate that Shechter's originally proposed densities and performance parameters were grossly overestimated. Furthermore, it is shown that, based on our predicted density value ranges, DTTO and iso-DTTO could match or substantially outperform the best state of the art explosives, such as CL-20. Therefore, the synthesis of DTTO and iso-DTTO should be further pursued.